The grim assessment that the deportations would be a death sentence was first made last month by likely 2016 Democratic presidential candidate Maryland Gov. Martin O'Malley.

His comment riled the White House, which was scrambling to deal with the crisis of thousands of unaccompanied alien children arriving in the U.S., most of whom President Obama had initially said he planned to deport. Presidential front-runner Hillary Rodham Clinton spoke similarly.

But a backlash from liberal immigrant advocacy groups forced him to retrench. He is under intense pressure from liberal and Hispanic groups to use executive orders this summer to further ease immigration laws, a move that would have potentially explosive political consequences.

Coming from Ms. Wasserman Schultz — a Florida congresswoman whose job leading the DNC includes cheerleading for Mr. Obama — the comment reveals divisions and confusion within the Democratic Party over a key issue heading into midterm elections.

A Democrat who is facing voters said Thursday that the nation should get “out of the executive order business” when it comes to strengthening the immigration system.

U.S. Senate candidate Michelle Nunn said at a forum hosted by the Georgia Chamber of Commerce that the tricky issue would be better solved if Mr. Obama does not feel the need to sidestep Congress.

“We need to have Congress and the president work together,” said Ms. Nunn, the daughter of Democratic former Sen. Sam Nunn. “We need to get out of the executive order business and into the compromising, collaboration and partnership business in Washington.”

Ms. Nunn is running against businessman David Perdue for the seat being vacated by retiring Republican Sen. Saxby Chambliss. She is seen as one of the Democrats’ best chances of picking up a GOP-held seat in the 2014 midterm elections.

The Wasserman Schultz flap grew out of an interview with Fusion’s Jorge Ramos, in which the DNC chief voiced enthusiastic agreement with Mr. O'Malley’s comments that deporting these unaccompanied minors is an unacceptable death sentence.

“Not only do I agree with him,” Ms. Wasserman Schultz said, adding that she had heard first-person accounts that proved it was true.

She said that during a tour of a shelter for the unaccompanied alien children, she had met a boy who had been kidnapped in Mexico, forced into the drug trade and shot in the arm. She said the boy pleaded to her: “If you send me back, I’m not going to survive.”